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Displaying 41 – 60 of 60

On the fundamental units of some cubic orders generated by units

Jun Ho Lee, Stéphane R. Louboutin (2014)

Acta Arithmetica

Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic polynomials...

On the group of circular units of any compositum of quadratic fields

Zdeněk Polický (2009)

Acta Arithmetica

On the Hilbert $2$ -class field tower of some imaginary biquadratic number fields

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini, Idriss Jerrari (2021)

Czechoslovak Mathematical Journal

Let $𝕜 = ℚ (\sqrt{2}, \sqrt{d})$ be an imaginary bicyclic biquadratic number field, where $d$ is an odd negative square-free integer and $𝕜_{2}^{(2)}$ its second Hilbert $2$ -class field. Denote by $G = Gal (𝕜_{2}^{(2)} / 𝕜)$ the Galois group of $𝕜_{2}^{(2)} / 𝕜$ . The purpose of this note is to investigate the Hilbert $2$ -class field tower of $𝕜$ and then deduce the structure of $G$ .

On the iwasawa invariants of totally real number fields.

Hiroshi Yamashita (1993)

Manuscripta mathematica

On the minimum of the unit lattice

Volker Kessler (1991)

Journal de théorie des nombres de Bordeaux

On the multiplicative independence of binomial coefficients

Jianguo Xia, Hourong Qin (2005)

Acta Arithmetica

On the number of solutions of linear equations in units of an algebraic number field.

K. Györy (1979)

Commentarii mathematici Helvetici

On the quadratic character of some quadratic surds.

Emma Lehmer (1971)

Journal für die reine und angewandte Mathematik

On the quantitative unit sum number problem-an application of the subspace theorem

Alan Filipin, Robert Tichy, Volker Ziegler (2008)

Acta Arithmetica

On the quartic character of quadratic units.

Emma Lehmer (1974)

Journal für die reine und angewandte Mathematik

On the relation between units and Jacobi sums in Prime cyclotomic Fields.

Francisco Thaine (1991)

Manuscripta mathematica

On the representation of units by cyclotomic polynomials

Veikko Ennola (1980)

Acta Arithmetica

On the Stark-Shintani units and the ideal class groups in the cyclotomic $ℤ_{p}$ -extensions of class fields over real quadratic fields

Tsuyoshi Itoh (2002)

Acta Arithmetica

On the Stickelberger Ideal and the Circular Units of an Abelian Field.

W. Sinnott (1980/1981)

Inventiones mathematicae

On the strongly ambiguous classes of some biquadratic number fields

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous (2016)

Mathematica Bohemica

We study the capitulation of $2$ -ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $𝕜 = ℚ (\sqrt{2 p q}, i)$ , where $i = \sqrt{- 1}$ and $p \equiv - q \equiv 1 (mod 4)$ are different primes. For each of the three quadratic extensions $𝕂 / 𝕜$ inside the absolute genus field $𝕜^{(*)}$ of $𝕜$ , we determine a fundamental system of units and then compute the capitulation kernel of $𝕂 / 𝕜$ . The generators of the groups ${Am}_{s} (𝕜 / F)$ and $Am (𝕜 / F)$ are also determined from which we deduce that $𝕜^{(*)}$ is smaller than the relative genus field ${(𝕜 / ℚ (i))}^{*}$ . Then we prove that each...

Currently displaying 41 – 60 of 60

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Displaying 41 – 60 of 60

On the fundamental units of some cubic orders generated by units

On the group of circular units of any compositum of quadratic fields

On the Hilbert $2$ -class field tower of some imaginary biquadratic number fields

On the iwasawa invariants of totally real number fields.

On the minimum of the unit lattice

On the multiplicative independence of binomial coefficients

On the number of solutions of linear equations in units of an algebraic number field.

On the quadratic character of some quadratic surds.

On the quantitative unit sum number problem-an application of the subspace theorem

On the quartic character of quadratic units.

On the relation between units and Jacobi sums in Prime cyclotomic Fields.

On the representation of units by cyclotomic polynomials

On the Stark-Shintani units and the ideal class groups in the cyclotomic $ℤ_{p}$ -extensions of class fields over real quadratic fields

On the Stickelberger Ideal and the Circular Units of an Abelian Field.

On the strongly ambiguous classes of some biquadratic number fields

On the structure of the group scheme $ℤ {[ℤ / p^{n}]}^{\times}$

On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field

On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1

On units and fundamental units.

On Washington group of circular units of some composita of quadratic fields

Currently displaying 41 – 60 of 60